1.1.5.5 Rate equations for steady-state laser oscillators

In the oscillator system, two counter-propagating traveling waves J +, J − appear, see Fig. 1.1.11, which are amplified by an intensityand z-dependent gain coe cient according to (1.1.58a), (1.1.58b):

For the two traveling waves the boundary conditions at the mirrors are:

J +(z = 0) = J −(z = 0)R1 ,

J −(z = ) = J +(z = )R2 .

The combination of (1.1.91a) and (1.1.91b) yields [81Ver]:

J +(z)J −(z) = const. ,

a useful relation for analytical solutions. The gain coe cient is saturated by both waves. In steady state (1.1.84)/(1.1.87) hold with J = J + + J −, depending on the level system and on the type of broadening. For homogeneous broadening a solution is given in [81Ver]. In general, numerical calculations are necessary. For optimization a diagram is o ered in [92Koe]. The intensity rate equations are very useful for laser design and optimization, but deliver no spectral e ects such as line width [58Sch, 74Sar, 95Man], mode competition [86Sie, 00Dav], mode hopping [86Sie, 64Lam, 74Sar], or intensity-dependent frequency shifts (Lamb dip) [64Lam]. Multimode oscillation can be described by rate equations with restrictions [64Sta, 63Tan, 93Sve].

1.1.6 Line shape and line broadening

Shape and width of the spectral response of the two-level system depend on the special stochastic perturbation processes, in detail discussed by [81Ver, 86Eas]. An easy-to-read introduction is given by [86Sie, 00Dav].

Landolt-B¨ornstein

New Series VIII/1A1